We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally L...We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.展开更多
This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditio...This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.展开更多
基金Supported by the National Natural Science Foundation of China (11761038)Science and Technology Project of Department of Education of Jiangxi Province (GJJ180583)。
基金Supported by the National Natural Science Foundation of China(10701066,10671084)the Natural Science Foundation of Henan Education Committee(2007110037)
基金supported by the National Science Foundation of China (11001063, 10971043)the Fundamental Research Funds for the Central Universities (HEUCF 20111134)+2 种基金China Postdoctoral Science Foundation Funded Project (20110491032)Heilongjiang Provincial Science Foundation for Distinguished Young Scholars (JC200810)Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803)
文摘We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.
基金supported by Anhui Provincial Nature Science Foundation(1208085MA13)the Research Fund for the Doctoral Program of Higher Education(20103401120002,20113401120001)+1 种基金211 Project of Anhui University(02303129,KJTD002B,02303303-33030011,02303902-39020011)the Key Foundation of Anhui Education Bureau(KJ2012A019)
基金The NSF(11271154)of Chinathe Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education+1 种基金the 985 program of Jilin Universitythe DR Fund(150152)of Henan University of Technology
文摘This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.
